Other top Republicans have gone so far as to pledge support for the Democratic nominee, Hillary Clinton.

On Wednesday, the Clinton campaign touted a list of Republicans and independents that are supporting the Democrat.

The list included Rep. Richard Hanna (R-N.Y.), former New York City Mayor Michael Bloomberg, former Sens. David Durenberger (R-Minn.) and Larry Pressler (R-S.D.), former Reps. Connie Morella (R-Md.) and Chris Shays (R-Conn.), former U.S. ambassador and Director of National Intelligence John Negroponte, Hewlett-Packard CEO Meg Whitman, and others.

Johnson has been aiming to make the debate stage by getting at least 15 points in the national polls by September. The Libertarian candidate is now polling at around 8 percent.